On probabilistic networks for selection, merging, and sorting

T. Leighton, Y. Ma, T. Suel

    Research output: Contribution to journalArticle

    Abstract

    We study comparator networks for selection, merging, and sorting that output the correct result with high probability, given a random input permutation. We prove tight bounds, up to constant factors, on the size and depth of probabilistic (n, k)-selection networks. In the case of (n, n/2)-selection, our result gives a somewhat surprising bound of Θ(n log log n) on the size of networks of success probability in [δ, 1 - 1/poly (n)], where δ is an arbitrarily small positive constant, thus comparing favorably with the best previously known solutions, which have size Θ(n log n). We also prove tight bounds, up to lower-order terms, on the size and depth of probabilistic merging networks of success probability in [δ, 1 - 1/poly(n)], where δ is an arbitrarily small positive constant. Finally, we describe two fairly simple probabilistic sorting networks of success probability at least 1 - 1/poly(n) and nearly logarithmic depth.

    Original languageEnglish (US)
    Pages (from-to)559-582
    Number of pages24
    JournalTheory of Computing Systems
    Volume30
    Issue number6
    StatePublished - Nov 1997

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    Sorting
    Merging
    Sorting Networks
    Logarithmic
    Permutation
    Output
    Term

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics
    • Mathematics(all)

    Cite this

    Leighton, T., Ma, Y., & Suel, T. (1997). On probabilistic networks for selection, merging, and sorting. Theory of Computing Systems, 30(6), 559-582.

    On probabilistic networks for selection, merging, and sorting. / Leighton, T.; Ma, Y.; Suel, T.

    In: Theory of Computing Systems, Vol. 30, No. 6, 11.1997, p. 559-582.

    Research output: Contribution to journalArticle

    Leighton, T, Ma, Y & Suel, T 1997, 'On probabilistic networks for selection, merging, and sorting', Theory of Computing Systems, vol. 30, no. 6, pp. 559-582.
    Leighton, T. ; Ma, Y. ; Suel, T. / On probabilistic networks for selection, merging, and sorting. In: Theory of Computing Systems. 1997 ; Vol. 30, No. 6. pp. 559-582.
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